Geological models are very useful tools for studying the subsoil, especially for oil field exploration or exploitation. One attempts to build a geological model that best represents the structure and behavior of a reservoir from measurements conducted on the surface (especially seismic measurements) or in wells (logs), or from observations made on core samples taken from the wells. Of course, even when large numbers of measurements and samples are collected, construction of a three-dimensional model that faithfully reflects the structure and behavior of the studied area of the subsoil is not a realistic goal. This is why statistical methods are used to construct these models.
Traditional geostatistical methods are based on the use of variograms which are measurements of spatial variability at two points. These traditional methods are very limited, especially in their ability to represent the sometimes complex topology of the area studied. Multipoint methods have been proposed since the 1990s to overcome these limitations.
Multipoint statistics (MPS) techniques are used to model geological heterogeneities in a manner that reproduces natural systems while better reflecting the uncertainties of the model.
The data input of MPS simulation techniques include training images whose selection plays an important role in the reliability of the model obtained. A training image is defined in a three-dimensional grid (3D). It is chosen so that it represents patterns of geological heterogeneities that one can expect to encounter in the reservoir (see S. Strebelle, “Conditional Simulation of Complex Geological Structures Using Multiple-Point Statistics”, Mathematical Geology, Vol. 34, No. 1, 2002, p. 1-21).
In the early days of the MPS technique, a stationary training image was used defining a conceptual representation of a sedimentary system, obtained from a sketch drawn by a geologist or from an object-based simulation. Newer algorithms allow MPS simulations using non-stationary training images, combining them with auxiliary training images (see T. L. Chugunova & L. Y. Hu, “Multiple-Point Simulations Constrained by Continuous Auxiliary Data”, Mathematical Geosciences, Vol. 40, No. 2, 2008, pp. 133-146).
Training images can correspond to a simplified representation of a contemporary analogue, obtained by an image processing technique applied to satellite photographs of a region of the world which, in the opinion of geological experts, has characteristics similar to those of the region with previously formed sedimentary deposits found within the subsoil study area. For example, various satellite images are processed and then stacked to form a three-dimensional representation which will serve as a training image.
Often, the study of a particular geological area includes drilling one or more wells in this area in order to collect measurements (logs) and/or samples. It is then possible to verify whether the 3D training image seems to be consistent with the well data available, in order to validate the training image or indicate that it needs to be modified. A training image which is not consistent with the well data is likely to provide a poor representation of the heterogeneities during simulations.
Methods for the validation of vertical heterogeneities in training images have been proposed by J. B. Boisvert, J. Pyrcz and C. V. Deutsch, in “Multiple-Point Statistics for Training Image Selection”, Natural Resources Research, Vol. 16, No. 4, December 2007, p. 313-320. Multipoint statistics such as the multipoint density function (MPDF) are calculated along a dimension based on the well data and on the training image. If there is a good correspondence between the two MPDF functions, the training image is considered to be consistent with the well data.
An object of the present invention is to enhance the methods for generating and validating training images. It is desirable to be able to validate a training image relative to well data without being limited to statistical estimates parallel to a well.